Fibonacci链的电子结构特性

对由递推关系S_m+1={S_m|S_m-1}生成的Fibonacci链,从Anderson紧束缚模型出发,用负本征值理论及三对角高阶厄米矩阵本征值理论,对电子的态密度和能级结构进行数值研究,直观简洁地论证其三分叉的能带结构.用重整化群方法,结合散射理论,研究链中电子的局域长度和输运系数,发现具有不同局域属性的能态.一些特定的能量区间值存在扩展态,其相应的输运系数接近1.绝大部分能量对应的电子具有很小或几乎为零的局域长度,说明链中存在相当数量的局域态.定性得出电子输运系数随Fibonacci链参数变化的规律.

Electronic Structure of Fibonacci Chains

For a Fibonacci chain constructed recursively with S_(m 1)={S_m|S_(m-1)},in a tight-binding model of single electron,we investigate numerically density of electronic states and electronic energy band structure with negative eigenvalue theory and three diagonally symmetric matrixes.Trifurcating structure of energy band of the system is demonstrated.With renormalization-group method and scattering theory,we study localization length and transmission coefficients of electronic states in a chain.At particular eigen-energies,extend states with localization lengths greater than size of the system are found and transmission coefficient is equal nearly to 1.At most eigen-energies, corresponding electronic states are localized states due to short localization length.In addition,relations between transmission coefficients and parameters of Fibonacci chain are qualitatively investigated.